Problem: What is the value of the following logarithm? $\log_{125} 5$
If $b^y = x$ , then $\log_{b} x = y$ Notice that $5$ is the cube root of $125$ That is, $\sqrt[3]{125} = 125^{1/3} = 5$ Thus, $\log_{125} 5 = \dfrac{1}{3}$.